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In this paper, we will describe the experience of the authors in using process-oriented guided inquiry learning (POGIL) in calculus at four institutions across the USA. We will briefly examine how POGIL compares to and fits in with other kinds of inquiry-based learning approaches. In particular, we will first discuss the unique structure of a POGIL activity, which includes a model and a learning cycle of specific types of questions. We then turn to a discussion of the particular characteristics of a classroom implementation of a POGIL activity, including facilitation strategies an instructor might use, the importance of specified student roles in groups, and different ways of reporting out. Finally, we provide some preliminary data on student pass rates in non-POGIL and POGIL calculus classrooms in the participating institutions. Throughout the paper, we use examples from student dialogues as groups were working through POGIL activities developed for Calculus I by the authors.

The photochemical reactions of cyclooctadienone 6 have been studied as a mode of entry to a cyclopentyl−oxyallyl system. Irradiation of cis,cis-2,7-cyclooctadienone 6 results in isomerization to cis,trans-2,7-cyclooctadienone 24. The strained dienone 24 is stable at −70 °C, but undergoes conrotatory cyclization at temperatures above −30 °C to the cis-bicyclo[3.3.0]oxyallyl system 25. The density functional theory (DFT) structural optimizations for 6, 24, and 25 at the 6-31G* B3LYP level yielded energies, selected geometric parameters, and charge/spin population data. The oxyallyl intermediate reacts with vinyl ethers in a stepwise fashion to give bridged and fused tricyclic products with defined stereochemistry at the ring junctures. Simple alkenes react with 25 in a concerted ene reaction to give bicyclic products. An explanation is offered to harmonize the traditional zwitterionic view of oxyallyl systems with the current computational assessment of oxyallyls as diradical species.

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